Solar Photovoltaic Water Heating System

ABSTRACT

A solar photovoltaic water heating system is disclosed having a photovoltaic solar panel array, a storage tank containing water to be heated, a resistance heating element in the water to be heated. The water heating system matches the load resistance of the resistance heating element to the power that is available from the photovoltaic solar panel array in order to maximum energy transferred to the water in the storage tank.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 61/733,595, filed Dec. 5, 2012, which is incorporated herein byreference.

FIELD OF THE INVENTION

The invention relates to a direct current (DC), photovoltaic (PV) waterheating system. In particular, the invention is a photovoltaic waterheating system that controls the electrical energy used to heat thewater.

BACKGROUND OF THE INVENTION

Solar water heaters are known in the prior art. Kemp U.S. Pat. No.451,384, entitled, “Apparatus for Utilizing the Sun's Rays for HeatingWater,” discloses a solar water heating system that comprises a seriesof large diameter pipes connected in series in a wooden box, insulatedwith sand, and covered with green house glass panes. The pipes containeda volume of water that was directly heated by solar irradiance duringthe day for use in the evening. Subsequent to the Kemp patent, animproved solar water heating system comprised a separate solar collectorand a storage tank. The solar collector used the decrease in the densityof the water when heated to move water into the tank. This arrangementcreated a thermo-siphonic flow. Solar water heating systems have beenevolving along those same technological lines ever since. Essentially,there is a tank, a collector, and a means to move heat energy from thecollector to the tank.

Fanney et al. U.S. Pat. No. 5,293,447, titled “Photovoltaic Solar WaterHeating System”, issued in 1994, discloses a solar water heating systemthat uses solar generated electricity from photovoltaic panels to powerspecialized electric resistance heating elements that are fully immersedin the water heater tank. The resistance heating elements are connectedin various parallel combinations, directly to the DC output of thephotovoltaic solar panels. A computer control system selects theconfiguration of resistance elements to match the electric power outputcharacteristics of the photovoltaic panels. The computer control systemmeasures the power characteristics of the photovoltaic panels andoperates electrical/mechanical relays that provide the direct connectionof the DC power from the photovoltaic array to the resistance heatingelement combinations. The heating element combinations are determined toextract the optimum amount of power from the photovoltaic array. Thesolar water heating system of the Fanney et al. patent is, however,limited to a maximum of 7 combinations of resistance and thosecombinations are not mathematically optimized to achieve even stepchanges in power delivery from the PV panel array.

Ashkenazy United States Patent Application Publication No. 20120187106,entitled “Photovoltaic Heater”, filed on Mar. 29, 2012, discloses aphotovoltaic heating system that relies on an inverter device for theconversion of direct current from a photovoltaic solar array toalternating current (AC) to power a conventional resistance heatingelement. DC to AC inverters have been used in PV systems for homes formany years to provide AC power for the various loads and appliancesincluding resistance water heaters. The Ashkenazy Application furtherdiscloses a switching circuit that disconnects the inverter's AC powerfrom the resistance heating elements and connects the AC power from theelectrical grid to the resistance heating elements. Consequently, theresistance heating elements are switched between one AC power source ofa variable level (solar) to another AC power source of a known andconstant level (electrical grid).

Yet another patent Thomasson United States Patent ApplicationPublication No. 2009/0188486, entitled “PV Water Heater with AdaptiveControl”, filed Jan. 24, 2008, discloses a method to detect hot waterusage, and interact with the PV that limits the energy delivery to thewater heater as a function of hot water usage.

SUMMARY OF THE INVENTION

The solar photovoltaic water heating system of the present inventioncomprises a solar PV array consisting of PV panels, a water storage tankfor storing heated water, resistance heating elements in the water tankfor heating the water, and a programmable control system for deliveringDC power from the PV panels to the resistance heating elements.

In overcoming the deficiencies of the prior art solar heating systems,the solar photovoltaic water heating system of the present inventionassures safety for the users of the hot water and assures safety inconnection with the use of direct electric current. The solarphotovoltaic water heating system is an advancement over other DC powerpowered direct PV heating systems in that the present invention employsformulae and methods for more accurately determining power output fromthe PV panels of the PV array in order to optimize energy deliver over awider range of operating conditions.

A feature of the present invention is the programmable control systemthat switches or redirects power available from the PV panels of the PVarray when the hot water load demand has been met.

A further feature of the present invention is a method implemented bythe control system that causes the photovoltaic water heating system tostore higher temperature water in the storage tank but then safelydelivers water at a lower temperature to the users of the hot water,thus allowing more energy to be stored in the tank during periods ofhigh solar irradiance.

Another feature of the present invention, the programmable controlsystem which includes a high temperature limit switch to insure watertemperatures do not exceed the practical operating limit of theparticular storage tank being used, thereby prolonging the life of thestorage tank and reducing warranty claims and issues.

An additional feature of the present invention is a method implementedby the control system for determining the best resistance values formultiple resistance heating elements that are used in varied connectionarrangements to maximize electrical energy delivery from the PV array.The method includes formulae to determine resistance values for theresistance heating elements that create more even steps in the powerpoint tracking of the energy delivered from the PV array to theresistance heating elements.

A further feature of the present invention is a method of accumulatingand storing data related to the energy delivered by the PV array to theresistance heating elements and to report that data to a remote dataacquisition system.

According to yet a further feature of the present invention is a methodto remotely access the control system for programming and data downloadsof stored information that users may determine is needed for otherpurposes.

Another feature of the present invention is a multiple resistanceheating element having four individual and discrete heating elements ina single assembly. The four prong resistance heating element isadaptable for use with either AC or DC electrical power.

An additional feature of the present invention is a structure for thefour pronged resistance heating element that can be used for either ACor DC electrical power.

Further objects, features and advantages will become apparent uponconsideration of the following detailed description of the inventionwhen taken in conjunction with the drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a solar photovoltaic water heatingsystem in accordance with the present invention.

FIG. 2 is a perspective view of a storage tank in accordance with thepresent invention.

FIG. 3 is a top plan view of the storage tank in accordance with thepresent invention.

FIG. 4 is a side elevation view of the storage tank in accordance withthe present invention.

FIG. 5 is a perspective view of a four pronged electrical resistanceheating element in accordance with the present invention.

FIG. 6 is a schematic diagram of a resistance value switching circuit inaccordance with the present invention.

FIG. 7 is a schematic diagram of another resistance value switchingcircuit in accordance with the present invention.

FIG. 8 is a data table showing irradiance performance of a typicalphotovoltaic panel.

FIGS. 9A and 9B is a flowchart of the control logic that is used in thephotovoltaic water heating system to control energy delivery from asolar panel array to the four pronged electrical resistance heatingelement.

FIG. 10 is a graph illustrating of a theoretical ideal power curve foran infinitely variable resistance load for a variable direct currentpower source and illustrating the power curve for the four prongedresistance heating element, connected in various combinations to providea variable resistance load.

FIGS. 11A and 11B are graphs illustrating two power point matchingcurves that illustrate step changes in power (wattage) as a function ofchanges in solar irradiance.

FIGS. 12A and 12B are data tables used in developing resistance valuesfor optimum operation of the photovoltaic water heating system inaccordance with the present invention.

FIGS. 13A-13C are data tables used in developing system resistancevalues for optimum operation of the photovoltaic water heating system inaccordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Turning to FIG. 1, a solar photovoltaic water heating system 1 is shown.The solar photovoltaic water heating system 1 includes a photovoltaicpanel array 31 consisting of individual solar photovoltaic panels 18, awater storage tank 10 with resistance heating elements 15, aprogrammable control system 16, and an alternating current power source32. The control system 16 is connected between the storage tank 10 andthe photovoltaic panel array 31 and the alternating current power source32 in order to control the delivery of power from either thephotovoltaic panel array 31 or the alternating current power source 32to the resistance heating elements 15. One of the heating elements 15may be a standard alternating current resistance heating element that isonly connected to the alternating current power source 32.Alternatively, both heating elements 15 may be alternating current anddirect current compatible, resistance heating elements such as theresistance heating element 15 shown in FIG. 5 and described below.

The photovoltaic panels 18 are conventional and produce direct currentpower when exposed to irradiance 19 from the Sun 20. The amount ofdirect current power produced by each photovoltaic panel 18 depends onthe level of irradiance 19 impinging on the photovoltaic panels 18.Consequently, because the level of irradiance 19 varies based on thetime of day and atmospheric conditions, the level of direct currentpower produced by each photovoltaic panel 18 varies accordingly. FIGS.13A-13C arc graphs that show the typical energy available from thephotovoltaic array 31 for different voltages, power levels, andaverages.

The water storage tank 10 is generally conventional and is shown inFIGS. 2-4. The water storage tank 10 includes a cold water inlet 22extending to near the bottom of the storage tank 10 for the introductionof cold water 12 into the storage tank 10. The storage tank 10 furtherincludes a hot water outlet 21 extending into the upper part of thestorage tank 10. A mixing valve 17 is connected to the hot water outlet21 and to a cold water shunt 33 in order to provide a mixture of hot andcold water to the hot water outlet 11, which in turn is connected to aconsumer water system (not shown). The mixing valve 17 isthermostatically controlled to ensure that the hot water 11 is not toohot for a consumer water system such as residential hot water system.The operation of the mixing valve 17 allows the water in the storagetank 10 to be raised substantially higher than a normal residentialconsumer water system thereby allowing the solar photovoltaic waterheating system 1 to store more energy in the storage tank 10. The waterstorage tank 10 further includes a cover 25 for housing and protectingthe control systems 16 and associated wiring. A pressure relief safetyvalve 23 is also connected to and in communication with the interior ofthe water storage tank 10. If the pressure inside the water storage tank10 exceeds a preselected level for the relief safety valve 23, therelief safety valve 23 opens so that the pressure inside the waterstorage tank 10 can be relieved.

The resistance heating elements 15 are located in the water storage tank10 at one or more levels to ensure consistency of the water temperaturein the water storage tank 10. As shown in FIG. 5, the resistance heatingelement 15 comprises, for example, four individual resistance heatingrods 29 connected through a stainless steel fitting 26. The resistanceheating rods 29 may be formed of stainless steel, inconel, carbon steel,or copper. The stainless steel fitting 26 is threaded into the side ofthe water storage tank 10 to form a water and pressure tight seal. Eachindividual resistance heating rod 29 has a pair of connecting wires 27that allow each resistance heating rod 29 to be individually connectedto either the photovoltaic array 31 or the direct current power source32 through a switching circuit, such as one of switching circuits 34(FIG. 6) and 35 (FIG. 7).

The switching circuits 34 and 35 are controlled by the control system 16in order to select the optimum load resistance, such as direct currentload resistance RloadDC 37 or RloadDC 39 for the direct current powersource 31 (photovoltaic array 31) or alternating current load resistanceRloadAC 36 or RloadAC 38 for the alternating current power source 32(public power grid). The switching circuit 34 illustrates a firstconfiguration and is configured to provide seven resistance values forthe direct current load resistance RloadDC 37 and one resistance valuefor the alternating current load resistance RloadAC 36. The switchingcircuit 34 comprises a DC switch 41, an AC switch 42, and a resistancearray including fixed value resistors R4, R6, R7, and R9 with theirassociated switches. The resistors R4, R6, R7, and R9 represent each ofthe four individual heating rods 29 in the resistance heating element15. The control system 16 opens and closes the DC switch 41, the ACswitch 42, and the switches associated with each of the resistors R4,R6, R7, and R9 in order to select the optimum direct current loadresistance RloadDC 37 for the direct current power source 31 or theoptimum alternating current load resistance RloadAC 36 for thealternating current power source 32. Selection of the optimum loadresistance RloadDC 37 or RloadAC 36 maximizes the energy delivered tothe water in the water storage tank 10 by either the direct currentpower source 31 or the alternating current power source 32.

Likewise the switching circuit 35 illustrates a second configuration andis configured to provide 14 resistance values for the direct currentload resistance RloadDC 39 and one resistance value for the alternatingcurrent load resistance RloadAC 38. The switching circuit 35 comprises aDC switch 43, an AC switch 44, and a resistance array including fixedvalue resistors R11, R12, R13, and R14 with their associated switches.The resistors R11, R12, R13, and R14 represent each of the fourindividual heating rods 29 in the resistance heating element 15. Thecontrol system 16 opens and closes the DC switch 43, the AC switch 44,and the switches associated with each of the resistors R11, R12, R13,and R14 in order to select the optimum direct current load resistanceRloadDC 39 for the direct current power source 31 or the optimumalternating current load resistance RloadAC 38 for the alternatingcurrent power source 32. Selection of the optimum load resistanceRloadDC 39 or RloadAC 38 maximizes the energy delivered to the water inthe water storage tank 10 by either the direct current power source 31or the alternating current power source 32.

With respect to configuration 1, illustrated by switching circuit 34 andby the table shown in FIG. 12A, the formula set forth below establishesthe values for the fixed resistors R4, R6, R7, and R9 (the resistanceheating rods 29 of the resistance heating element 15). Once the valuesfor the resistors R4, R6, R7, and R9 have been established, the controlsystem 16 runs an algorithm to open and close the switches in theswitching circuit 34 to produce the optimum load resistance for thepower source that is available. In order to determine the values for theresistors R4, R6, R7, and R9, the formula first solves for the singleresistor R4 (one of the four heating rods 29 of the heating element 15).The value for the resistor R4 is then used in a ratio determinationmethod, described in greater detail below, to determine the three otherfixed resistance values for resistors R6, R7, and R9 (the other three ofthe four heating rods 29 of the heating element 15). The fixedresistance values of resistors R4, R6, R7, and R9 are used by thecontrol system 16 in various single and parallel connection arrangementsto create up to seven different direct current load resistance valuesR1, R2, R3, R4, R5, R6, and R7, and one alternating current loadresistance value R8 (see table, FIG. 12A). The resistance values R1-R7are used in connection with the direct current power source 31, and theresistance value R8 is used in connection with the alternating currentpower source 32. The resistance value R8 is the optimum value for thealternating current power source 32, and the resistance value R8 is thelowest available resistance and results from the parallel connection ofall four fixed resistors R4, R6, R7, and R9 (resistance heating rods 29of the resistance heating element 15). R1 is the optimum resistancevalue for the direct current power source 31 where the direct currentpower source is delivering maximum energy at 1000 watts per square meterof solar irradiance 19. See FIG. 8, first line (resistance=23.82 ohms)and FIG. 12A (R1=23.82 ohms).

The formula for determining the value of the fixed resistor R4 forconfiguration 1 (FIG. 12A) is as follows:

P_(W)=Array Power in watts at solar irradiance level (w)

MPP=Maximum Power Point (MPP—the optimum transfer of energy from thepower source to the resistance load)

R=Load Resistance

W=Watts delivered to the load

W/m²=Watts per square meter of solar irradiance

V_(K)=Photovoltaic array operating MPP voltage (volts) @ 1000 W/m²

Photovoltaic array operating MPP source (amps) @ 1000 W/m²

V_(W)=Photovoltaic array MPP voltage at a stated level of solarirradiance (w)

I_(W)=Photovoltaic array MPP current at a stated level of solarirradiance (w)

M_(v)=Slope of linear equation for calculating Voltage (≈0)

B_(v)=y-intercept of linear equation for calculating Voltage (≈V_(W))

P _(W)=V_(W) I_(W)   Standard Power formula:

The majority of mono-crystalline photovoltaic panels follow theapproximation for input energy between 200 and 1000 W/m².

V _(W)≈M_(v) W+B_(v)

I_(W)(W/1000)I_(K)

Formula for determination of optimal value of R₄ is as follows:

R ₁=1/((1/R ₄)+(1/R ₆)+(1/R ₇))=V_(K) /I _(K)

I _(K) /V _(K)=(1/R ₄)+(1/2R ₄)+(1/4R ₄)→I _(K) /V _(K)=1.75/R ₄ →R₄=1.75(V _(K) /I _(K))

Once the value of R4 for configuration 1 (FIG. 12A) is determined, theratio formula is used to select the optimal resistance values of fixedresistors R6, R7, and R9:

R₄ is used to determine R₆, and R₇ wherein

R₆ is a multiple of two (2) times the value of R₄

R₇ is a multiple of four (4) times the value of the value of R₄.

R₉ is determined by inserting the derived value for optimal AC operationas follows:

-   -   W_(AC)=desired power output for alternating current power source    -   V_(AC)=voltage for the alternating current power source    -   I_(AC)=W_(AC)/V_(AC)    -   R_(AC)=V_(AC)/I_(AC) Example: W_(AC)=3500 watts

V_(AC)=240 volts

The calculation then proceeds as follows: I_(AC)(current)=3500/240=14.58 mps

R_(AC)=240/14.58=16.46

R ₉=1/((1/R _(AC))−(1/R ₄)−(1/R ₆)−(1/R ₇))*=1/((1/R _(AC))−(1.75/R ₄))

R ₈=1/((1/R ₄)+(1/R ₆)+(1/R ₇)+(1/R ₉))=R_(AC)**

R₇=4 R₄*

R₆=2R₄*

R ₅=1/((1/R ₇)+(1/R ₆))

R₄=Value of resistance to be determined using proprietary formula*

R ₃=1/((1/R ₄)+(1/R ₇))

R ₂=1/((1/R ₄)+(1/R ₆))

R ₁=1/((1/R ₄)+(1/R ₆)+(1/R ₇))

R₀=∞ (all off)

-   * (these are the fixed values of resistance for the four (4) pronged    heating element 15-   ** (the R₈ value being the optimum resistance for operation on grid    alternating current power)

With reference to FIGS. 6 and 12A, the direct current load resistanceRloadDC 37 and the alternating current load resistance RloadAC 36 forthe switching circuit 34 are selected by the switch configurationsdefined by the binary bits, in the column “Switch RS.” Each of thebinary bits indicates the status of the associated switches for thefixed resistors R4, R6, R7 and R9. For example, for the direct currentpower source 31, the control system 16, based on the output from directcurrent power source 31, closes the DC switch 41, opens the AC switch42, and sets the binary code to 1110. With the binary code set to 1110,the associated switches for fixed resistors R4, R6, and R7 are closed,and the direct current load resistance RloadDC 37 equals the parallelcombination of fixed resistors R4, R6, and R7, equals resistance R1, andequals 23.82 ohms (FIG. 12A, line R1). As a further example, for thealternating current power source 32, the control system 16 closes the ACswitch 42, opens the DC switch 41, and sets the binary code to 1111.With the binary code set to 1111, the associated switches for fixedresistors R4, R6, R7, and R9 are closed, and the alternating currentload resistance RloadAC 36 equals the parallel combination of fixedresistors R4, R6, R7 and R9, equals resistance R8, and equals 16.46 ohms(FIG. 12A, line R8).

With respect to configuration 2, illustrated by switching circuit 35(FIG. 7) and by the table shown in FIG. 12B, the formula set forth belowestablishes the values for fixed resistors R11, R12, R13, and R14 (thefour resistance heating rods 29 of the resistance heating element 15).Once the values for the resistors R11, R12, R13, and R14 have beenestablished, the control system 16 runs an algorithm to open and closethe switches in the switching circuit 35 to produce the optimum loadresistance for power source that is available. In order to determine thevalues for the resistors R11, R12, R13, and R14, the formula firstsolves for the single resistor R11 (one of the four heating rods 29 ofthe heating element 15). The value for the resistor R11 is then used ina ratio determination method, described in greater detail below, todetermine the three other fixed resistance values for resistors R12,R13, and R14 (the other three of the four heating rods 29 of the heatingelement 15). The fixed resistance values of resistors R11, R12, R13, andR14 are used by the control system 16 in various single and parallelconnection arrangements to create up to 14 different direct current loadresistance values R1, R2, R3, R4, R5, R6, R7, R8, R9, R10, R11, R12,R13, and R14 and one alternating current load resistance value R15 (seetable, FIG. 12B). The resistance values R1-R14 are used in connectionwith the direct current power source 31, and the resistance value R15 isused in connection with the alternating current power source 32. Theresistance value R15 is the optimum value for the alternating currentpower source 32, and the resistance value R15 is the lowest value andresults from the parallel connection of all four fixed resistors R11,R12, R13, and R14 (resistance heating rods 29 of the resistance heatingelement 15). R1 is the optimum resistance value for the direct currentpower source 31 where the direct current power source is deliveringmaximum energy at 1000 watts per square meter of solar irradiance 19.See FIG. 8, first line (resistance=23.82 ohms) and FIG. 12B (R1=23.82ohms).

The formula for determining the value of the fixed resistor R11 forconfiguration 2 (FIG. 12B) is as follows:

P_(W)=Array Power in watts at solar irradiance level (w)

MPP=Maximum Power Point (MPP-the optimum transfer of energy from thepower source to the resistance load)

R=Load Resistance

W=Watts

W/m²=Watts per square meter of solar irradiance

V_(K)=Photovoltaic array operating MPP voltage (volts) @ 1000 W/m²

I_(K)=Photovoltaic array operating MPP current (amps) @ 1000 W/m²

V_(W)=Photovoltaic array MPP voltage at a stated level of solarirradiance (w)

I_(W)=Photovoltaic array MPP current at a stated level of solarirradiance (w)

M_(v)=Slope of linear equation for calculating Voltage (≈0)

B_(v)=y-intercept of linear equation for calculating Voltage (≈V_(W))

P_(W)=V_(W) I_(W)   Standard Power formula:

The majority of mono-crystalline PV panels follow the approximation forinput energy between 200 and 1000 W/m².

V_(W)≈M_(v) W+B_(v)

I_(W)≈(W/1000)I_(K)

R_(K)≈Optimum resistance for Maximum Power delivery at 1000 W/m²

Formula for determination of optimal value of R₁₁ is as follows:

R ₁ =R _(K) =V _(K) /I _(K)=1/((1/R ₁₁)+(1/1.2R ₆₁)+(1.5/R ₁₁))

I _(K) /V _(K)=(1/R ₁₁)+(0.8333/R ₁₁)+(0.6666/R ₁₁)→I _(K) /V _(K)=2.5/R₁₁ →R ₁₁=2.5(V _(K)/I_(K))

Once the value of R11 for configuration 2 (FIG. 12B) is determined, theratio formula is used to select the optimal resistance values of fixedresistors R12, R13, and R14:

R₁₂ is a 1.20 ratio of R₁₁.

R₁₃ is a 1.50 ratio of R₁₁.

R₁₄ is a 2.00 ratio of R₁₁.

Thus creating the resistance values:

R₀=∞ (all off)

R1=1/((1/R11)+(1/R12)+(1/R13))

R2=1/((1/R11)+(1/R12)+(1/R14))

R3=1/((1/R11)+(1/R13)+(1/R14))

R4=1/((1/R12)+(1/R13)+(1/R14))

R5=1/((1/R11)+(1/R12))

R6=1/((1/R11)+(1/R13))

R7=1/((1/R11)+(1/R14))

R8=1/((1/R12)+(1/R13)) Not needed as the step difference is negligible

R9=1/((1//R13)+(1/R14))

R10=1/((1/R13)+(1/R14))

R11=Fixed resistance value derived using proprietary Formula of Claim1.*

R12=Fixed resistance value equal to 1.20×R11*

R13=Fixed resistance value equal to 1.50×R11*

R14=Fixed resistance value equal to 2.00×R11*

R15=1/((1/R11)+(1/R12)+(1/R13)+(1/R14))**

-   * these are the fixed values of resistance for the four (4) pronged    heating element-   ** this value is used for AC operation using grid power

With reference to FIGS. 6 and 12B, the direct current load resistanceRloadDC 39 and the alternating current load resistance RloadAC 38 forthe switching circuit 35 are selected by the switch configurations,defined by the binary bits, in the column “Switch RS.” Each of thebinary bits indicates the status of the associated switches for thefixed resistors R11, R12, R13, and R14. For example, for the directcurrent power source 31, the control system 16, based on the output fromdirect current power source 31, closes the DC switch 43, opens the ACswitch 44, and sets the binary code to 1010. With the binary code set to1010, the associated switches for fixed resistors R11 and R13 areclosed, and the direct current load resistance RloadDC 39 equals theparallel combination of fixed resistors R11 and R13, equals resistanceR6, and equals 35.72 ohms (FIG. 12A, line R6). As a further example, forthe alternating current power source 32, the control system 16 closesthe AC switch 44, opens the DC switch 43, and sets the binary code to1111. With the binary code set to 1111, the associated switches forfixed resistors R11, R12, R13, and R14 are closed, and the alternatingcurrent load resistance RloadAC 38 equals the parallel combination offixed resistors R11, R12, R13, and R14, equals resistance R15, andequals 19.85 ohms (FIG. 12B, line R15).

Turning to FIGS. 9A and 9B, the control system 16 is programmed toimplement the control method 50 that controls the selection of theoptimized resistance for either the direct current power source 18 orthe alternating power source 32. The control method 50 has a MainCommand Logic Routine 52, a Sampler Logic Subroutine 54 and a Read PowerSubroutine 56. The control method 50 begins at loop step 58 of the MainCommand Logic Routine 52. The internal processor of control system 16steps through the logic sequence continually while the system has powerapplied and is in operation. Using the example of the operationalresistance values of the 4 resistor configuration 2 of FIG. 12B, eachresistance value corresponds to a “Mode” of operation of the solarphotovoltaic water heating system 10. There are therefore 15 distinctoperating modes each corresponding to a lineup of resistors that havebeen connected in parallel to set a different resistance value dependingon the direct current power available for 14 of the modes and one modewhere all fixed resistance values R11, R12, R13, and R14 are switched onin parallel thereby creating an optimized resistance for operation ofthe resistance heating element 15 in the storage tank using powersupplied by the alternating current power source 32.

Starting from loop step 58 of the main command logic routine 52, theroutine 52 moves to step 60 where the routine 52 sets the resistance toMode 14 (R14 of configuration 2, FIG. 12B), the highest value for theresistance of the resistance heating element 15. From step 60, theroutine 52 moves to step 62, where routine 52 imposes a two seconddelay. From step 62, the routine 52 moves to step 64, and branches tostep 104 of the Read Power Subroutine 56. From step 104, the subroutine56 moves to step 106. At step 106, the subroutine 56 uses the highestresistance value R14 to read power available from the photovoltaic array31. The power (P) available from the photovoltaic array 31 is determinedby measuring the voltage (V) from the photovoltaic array 31 and thencalculating the power from the photovoltaic array 31 by using theformula Pcurrent=V²/R wherein resistance is a function of the Mode atthe time Pcurrent is determined. Once the current power (Pcurrent) fromthe photovoltaic array 31 has been determined at step 106, thesubroutine 56 moves to step 108 and branches to step 66 of the routine52.

At step 66, the routine 52 compares the previously determined power fromthe photovoltaic array 31 to the current power from the photovoltaicarray 31 (Pprevious=Pcurrent). From step 66, the routine 52 moves todecision step 68, where the routine 52 determines if the current Mode isless than 15 and the routine 54 at step 94 is sampling the power fromthe photovoltaic array 31 using combinations the fixed resistor R11,R12, R13, and R14 to create progressively lower resistances. If at step68 the routine 52 determines that the current Mode is less than 15 andsubroutine 54 at step 94 is sampling to a lower resistance, the routine52 follows the yes branch to step 72. If on the other hand, the routine52 determines that Mode is greater than 15 or the subroutine 54 issampling to higher resistances, the routine 52 follows the no branch tostep 70. At step 72, the routine 52 sets Mdiff=+1. The term “Mdiff”means the difference by which the Mode changes when determining the nextpower reading by means of subroutine 56. Particularly, at step 72 theroutine 52 decreases the resistance by reconfiguring the fixed resistorsR11, R12, R13, and R14 to create a lower value of total resistance.Lowering the resistance is accomplished by turning on the nextresistance value in parallel with the previous Mode resistance value,i.e changing from R14 to R13 in FIG. 12B (0001 to 0010).

If at step 68 the determination is no, then the routine 52 moves to step70 where the routine 52 determines if the Mode is greater than 1 andsampling is to a higher resistance. If at step 70 the routine 52determines that the Mode is greater than 1 and the subroutine for issampling toward higher resistances, the routine 52 follows the yesbranch to step 74. At step 74, the routine 52 sets Mdiff=−1, i.e. theroutine 52 subtracts one resistance value to change the Mode to a higherresistance. If at step 70 the condition is not satisfied, the routine 52follows the no branch to step 78, which then returns the routine 52 tothe beginning at step 58.

After the routine 52 has processed Mdiff at either step 72 or step 74,the routine 52 moves to step 76 that branches to step 80 of subroutine54. In the Sampler Logic Subroutine 54, the subroutine 54 setsMode=Mode+Mdiff. From step 82 of subroutine 54, the subroutine 54proceeds to step 84 where the subroutine 54 sets the resistorsassociated with the Mode (Mode+Mdiff). Particularly, the fixed resistorsR11, R12, R13, and R14 are selected in accordance with the switchconfigurations shown in FIG. 12B. From step 84, the subroutine 54proceeds to step 86 that imposes a 0.1 second delay. After the delay atstep 86, the subroutine 54 proceeds to step 88, and then branches tostep 104 of subroutine 56. The Read Power Logic Subroutine 56 againdetermines the power value for the photovoltaic array 31 as previouslydescribed. Once the subroutine 56, has completed its operation, controlis transferred from step 108 back to step 88 any of the subroutine 54.

From step 88, the subroutine 54 proceeds to step 90. At step 90, thesubroutine 54 determines if Pcurrent is greater than Pprevious. If atstep 90 Pcurrent is greater than Pprevious, the subroutine 54 followsthe yes branch to step 92. At step 92, the subroutine 54 setsMode=Mode+Mdiff. Once the Mode has been set at step 92, the subroutine54 proceeds to step 94 where the sampling direction of the resistance isswitched and a 0.1 second delay is imposed at step 96. From step 96, thesubroutine 54 moves to step 98. At step 98, the subroutine 54 setsMode=Mode−Mdiff. From step 98, the subroutine 54 proceeds to step 100,where the sampling direction for the resistance is again switched. Fromstep 100, the subroutine 54 proceeds to step 102, which returns to step76 of the routine 52. From step 76, the routine 52 proceeds to step 78,and then returns to the beginning at step 58.

If on the other hand, at step 90 Pcurrent is less than Pprevious, thesubroutine 54 follows the no branch to step 98. At step 98, thesubroutine 54 sets Mode=Mode−Mdiff. From step 98, the subroutine 54proceeds to step 100, where the sampling direction for the resistance isagain switched. From step 100, the subroutine for proceeds to step 102,which returns to step 76 of the routine 52. From step 76, the routine 52proceeds to step 78, and then returns to the beginning at step 58.Consequently, method 50 continues sampling the power from thephotovoltaic array 31 until a change is detected against the powertrend. The control determination and switching process continues byconstantly sampling values at varying time intervals as determined bythe change rate of solar irradiance.

The programmable control system 16 of the present invention alsomonitors the water temperature and the water pressure in the storagetank 10. Particularly, the storage tank 10 includes a temperature sensor28 and a pressure sensor 14. The temperature sensor 28 and the pressuresensor 14 are connected to the control system 16. When the watertemperature in the storage tank 10 falls below a preselected minimumtemperature, the control system 16 connects either the direct currentpower source 18 or the alternating current power source 32 to theresistance heating elements 15. Once the water temperature in thestorage tank tenant reaches a maximum temperature based on the datareceived from the temperature sensor 28, the control system 16disconnects either the direct current power source 18 or the alternatingfrom the resistance heating elements 15. Once the direct current powersource 18 has been disconnected from the resistance heating elements 15,the direct current power source 18 can be diverted to a direct currentpower takeoff 30 that can be used to charge batteries, to power aninverter, or to drive a second resistance heating load such as a hotwater space heating system. The control system 16 further monitors thedata from the pressure sensor 14 so that the pressure in the storagetank 10 remains in a preselected safe pressure range. If the pressure inthe water storage tank 10 rises above the preselected pressure range,the control system 16 disconnects either the direct current power source18 or the alternating current power source 32 from the resistanceheating elements 15. If the pressure continues to rise in the waterstorage tank 10, the pressure relief safety valve 23 will open relievingthe pressure in the storage tank 10. Further, if the pressure dropsbelow the preselected pressure range, the control system 16 disconnectseither the direct current power source 18 or the alternating currentpower source 32 from the resistance heating elements 15 so that thewater in the storage tank 10 does not begin to boil at a low-pressure.

The control system 16 is programmable, either through a direct interfaceor remotely through a remote interface, and can be programmed to collectoperating data including, but not limited to, the temperature andpressure data over time, the power delivered to the resistance heatingelements 15, the amount of energy delivered to the resistance heatingelements 15 by the direct current power source 18 over time, and theamount of energy delivered to the resistance heating elements 15 by thealternating current power source 32 over time. Such data can be storedlocally by the control system 16 or it can be transmitted to a remotedata acquisition system (not shown) either over a wired network or awireless network. Further, with advanced internal programming, thecontrol system 16 is capable of learning to optimize energy delivery.For example, the control system 16 can monitor the time of day, thesolar irradiance 19, and the temperature of the storage tank 10 andthereby determine the optimal time to switch from the direct currentpower source 18 to the alternating current power source 32 by means ofthe switching circuit 34, switches 41 and 42 or by means of theswitching circuit 35, switches 43 and 44. Further, the time of the day,from around 2-3 pm to 5-6 pm depending on geographic location, offersthe greatest chance that the solar array 31 will provide sufficientenergy to bring the storage tank 10 to its maximum temperature in whichcase the alternating current power source 32 will not be used therebyincreasing the efficiency of the solar photovoltaic water heating system1. The time periods above are also the less likely time periods in whicha high consumption of hot water will be used while the sun is still out.

Turning to FIG. 10, the graph shows an idealized power curve (power fromthe direct current photovoltaic power source 31 versus load resistance)that defines the maximum power point, i.e., the point of optimumtransfer of energy from the power source to the resistance load wherethe load resistance is infinitely variable. The graph in FIG. 10compares the idealized power curve to the operating curve for the solarphotovoltaic water heating system 1 of the present invention.Particularly, the graph in FIG. 10 shows that by matching the resistanceusing the switching circuits 34 and 35, the performance of the solarphotovoltaic water heating system 1 of the present invention closelytracks the idealized power curve.

FIGS. 11A and 11B show plots of the step changes in the load resistancethat occurs when using the formula and method of the present invention.To maximize energy delivery by maximum power point matching, the stepsin the changes of the load resistance must be in as equal incrementedvalues as possible. Resistance values that have changes that createanything other than a smooth curve will vary the load resistance aboveor below the maximum power point matching for a given level of solarirradiance. Resistance values that cause points to deviate from a smoothcurve plotting will cause losses of energy delivery to the medium beingheated.

FIGS. 13A-13C are examples of data tables derived from measured andpublished performance information regarding photovoltaic panels. Thedata then is used to determine the various photovoltaic water heatingsystem operating parameters, which in turn is used to determine theresistance values of the heating rods 29.

While the invention has been described in connection with heating water,the invention has applicability to heating other media for storingenergy. Further, while this invention has been described with referenceto preferred embodiments thereof, it is to be understood that variationsand modifications can be affected within the spirit and scope of theinvention as described herein and as described in the appended claims.

We claim:
 1. A solar photovoltaic water heating system comprising: a. asolar photovoltaic panel for producing direct current power; b. a waterstorage tank including: i. a cold water inlet; ii. a hot-water outlet;and iii. a variable resistance heating element having an electricalresistance; and c. a control system connected between the solarphotovoltaic panel and the variable resistance heating element andconfigured to vary the resistance of the variable resistance heatingelement to match the direct current power supplied by the solarphotovoltaic panel.
 2. The water heating system of claim 1, wherein thevariable resistance heating element comprises an array of individualfixed resistance heating rods and the control system is configured toswitch the array of individual fixed resistance heating rods into aplurality of single and parallel connections in order to vary theresistance of the variable resistance heating element.
 3. The waterheating system of claim 2, wherein the water heating system furtherincludes a switching network connected to the individual fixedresistance heating rods and controlled by the control system to switchthe array of individual fixed resistance heating rods into a pluralityof single and parallel connections in order to vary the resistance ofthe variable resistance heating element.
 4. The water heating system ofclaim 1, wherein the water heating system further comprises aalternating current power source for producing alternating current powerconnected to the control system, and wherein the control system isconfigured to alternatively connect the direct current power from thesolar photovoltaic panel or the alternating current power from thealternating current power source to the variable resistance heatingelement.
 5. The water heating system of claim 1, wherein the waterheating system further includes a mixing valve having a first hot waterinlet connected to the hot water outlet, a second cold water inletconnected to the cold water inlet via a cold water shunt, and a mixingvalve outlet for delivering a mixture of hot and cold water to aconsumer water system and wherein the control system controls the mixingvalve and therefore the mixture of hot and cold water to the consumerwater system.